Mechanical resonator, such as piezoelectric crystal devices



M. E. A. BRUZAU ET AL 2,203,322

, SUCH AS PIEZOELECTRIC CRYSTAL DEVICES 2 Shets-Sheet 1 Filed Jan. 22, 1937 ZZZVVV man. eel/2,40 .9. V4 M/EAIO EL 6000 v June 4, 1940.

MECHANICAL RESONATOR 'June 4, 1940. 2,203,322

, sucn AS PIEZOELECTRIC CRYSTAL DEVICES M. E. A. BRUZA U ET AL MECHANICAL RESONATOR Filed Jan. 22, 1937 2 Sheets-Sheet 2 Patented June 4, 1940 UNITED STATES FATENT OFFECE MECHANICAL RESONATOR, SUCH AS PIEZO- ELECTRIC CRYSTAL DEVICES New York, N. Y.

ApplicationJanuary 22, 1937, Serial No. 121,858 In France January 30, 1936 5 Claims.

The present invention relates to improvements in means for supporting vibrating mechanical elements such as piezoelectric devices.

One object of the invention is to provide means for reducing the influence of harmful modes of vibration in vibrating mechanical elements.

Another object of the invention is to provide means for reducing the influence of temperature variations on the said vibrating elements.

Another object of the invention is to provide improved supporting means for piezoelectric and like mechanically vibrating elements which may be employed as frequency standards.

The invention will be described as exemplified in a device utilizing piezoelectric substances such as the well known quartz crystals.

The features of the invention will be understood from a reading of the following explanation and description of preferred embodiments based on the attached drawings in which:

Fig. 1 represents a curve of variation of fre quency with temperature of a normal piezoelectric quartz plate in which vibratory movements are permitted to be set up along the electrical axis of the crystal;

Fig. 2 shows schematically a theoretical device in which the effect of a harmful mode is reduced;

Fig. 3 represents a curve of frequency variation with temperature of the piezoelectric quartz plate employed in the case shown in Fig. 1, but provided with a device employing features of the invention.

Fig. 4 shows an arrangement for maintaining in a suitable position a bevelled quartz plate in accordance with certain features of the invention;

Fig. 5 is a sectional longitudinal view of a piezoelectric resonator employing features of the invention;

Fig. 6 represents a transverse section of said resonator;

Fig. 7 is a longitudinal sectional view of another embodiment of the piezoelectric resonator employing features of the invention;

Fig. 8 represents an end view of the resonator shown in Fig. 7, and, finally,

Fig. 9 is a side elevation of a mechanical adjusting device provided in the resonator of Fig. '7.

The curve in Fig. 1 represents a quartz plate whose principal sectional plane contains the electric axis, but is inclined with respect to the optical axis at a certain angle suitably chosen to reduce the influence of temperature variations on the frequency. The plates of a crystal cut in the above fashion are in efiect the seat of shear vibrations propagated through the thickness of the plate and reflected by the two principal faces. An elastic standing wave is thus produced whose length is equal to twice the thickness of the plate. This vibration is characterised by a zero temperature coefficient and would, if it were the only vibration, produce vibrations of a frequency independent of the temperature.

However, the shear deformation gives rise to a compressional deformation along the electrical axis contained in the plane of the quartz plate. This gives rise to a secondary vibration which, owing to reflection, produces a second system of standing waves. Along the thickness there is an elastic half shear wave and along the electrical axis there are several elastic half compression waves. There is a coupling between the fundamental of the vibration along the thickness and a harmonic or partial harmonic of the vibration along the electrical axis. This vibration along the electrical axis is characterised by a negative temperature coefficient and will influence the frequency of the vibration because of the coupling of the shear and compressional vibrations. It will give rise to discontinuities of frequency such as shown by the curve of Fig. l for a particular plate subjected to the test. This curve graphically represents the M from the normal frequency plotted as ordinates against the temperature 6 plotter as abscissae.

Said discontinuities would not be produced if the plate were aperiodic with respect to the vibrations along the electrical axis of the quartz, that is to say, if the diameter of the plate were infinite. Any compressional deformation which in effect comes from the centre would in such case never reach the edges.

The problem thus consists in replacing a standing wave by a travelling wave. In terminated two conductor alternating current transmission lines a similar problem has been solved by terminating the line in a resistance equal to the characteristic impedance of the line.

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A similar condition may be realised for a mechanical vibrating system. For an infinite bar of any elastic substance such as quartz or steel, etc., having a modulus of elasticity E and a density p, there exist between the displacement c of any section on either side of its position of equilibrium and the internal pressure P caused by its distortion, the relations:

$1 E ai ax where X is the distance from the origin to the point under consideration, and t is the time from some arbitrary instant of reference. Differentiating the first of the above equations with respect to X and combining them, there is obtained the following equation:

12 rm or p 6X This latter equation represents a wave motion Whose speed of propagation V is ment 6 which is hereinafter referred to as the vibratory speed, 1), are joined by the relations:

which may be differentiated with respect to X and t respectively, and then combined to give the following equation:

an? 22 Di p 5X2 Consequently, if a simple harmonic disturbance occurs at a point of the bar and is propagated in both directions, without being reflected since the bar is infinite, then at a distance X from the origin, '0 and 1a are given by the relations:

where '0. represents the maximum value of c, and 0) represents the angular frequency of the assumed disturbance. These equations show that the vibratory speed c and the pressure p are in phase and that there is between them the true proportional relation in which the quantity 1/1 plays the part of a mechanical characteristic impedance having the dimensions of a coefiicient of viscosity divided by a length.

Now it is well known that a viscous system also offers a resisting force which is in phase with the velocity of the impressed motion and proportional thereto. Therefore, if a viscous system is coupled to the end of a given finite elastic bar, it will (if its coefiicient of viscosity and dimensions have the correct values) present to the bar exactly the same forces as would be presented by a further similar bar of infinite length coupled to form an extension of the given bar. Consequently, if we terminate a finite bar of quartz or any elastic substance by a suitable viscous system, the same aperiodicity as if the bar were infinite will be realised. Fig. 2 shows schematically such an arrangement. B represents a block having a section S and a height h of a viscous substance having a viscosity coefficient v fixed at its base to an immovable mass M and at its top to a lamina P connected to the end of the bar Q whose transverse section is 5. Thus the base of the viscous block B will have no movement while its top will vibrate on either side of its position of equilibrium at the same frequency as the extremity of the bar Q. The speed of vibration v 01' the top of the block B will thus be the same as that of the bar Q. There will be a gradient of vibratory speed depending on the height h of the viscous block, which gradient will be assumed to be constant. The relation:

Ov v

will then hold and the tangential force 1 to be applied to the top of the block 13 to produce its movement may be expressed in the following two different ways:

which will give between p and o the relation:

in which the quantity has the dimension of a coefficient of elasticity divided by a length. It has, therefore, the same dimensions as the characteristic impedance of the bar.

Consequently, if we realise the condition of equality between these two relations, that is the missing part of the bar, which would lie beyond the sectioned element if the bar were infinite, may be considered to be replaced by an equivalent viscous system in which will be dissipated the power which passes through the sectional element per second, i. e. the power which, in the case of an infinite bar, would go on to infinity. The bar will thus be the seat of a travelling and no longer of a standing Wave.

If the condition of equality between these two expressions is practically realised by the removal of a portion of the bar Q, a finite bar will be obtained which will be equivalent to the infinite periodic bar. The finite bar will be the seat of a travelling wave.

Since only approximate equalization is possible, the reflected wave will not be completely eliminated, but its intensity will be less than that of the incident wave, and the vibratory condition of the bar may be considered as the superposition of a travelling wave on a weak standing wave. The quartz discs can thus be considered as quasi aperiodic.

In order to attain one object, we may employ one of a number of well-known mechanical dissipating systems such as mechanical transmission lines the characteristic impedance of which is adjusted or matched to that of the piezoelectric element. Obviously, the transmission lines must be adapted to cooperate with the vibrating element.

Experience has shown that the above calculaa Tip tions render it possible suitably to dimension the damping substance, but in many cases one may rest content with a certain approximation sufficient to obtain curves showing the variation of frequency with temperature which are without discontinuity and without great variations. Fig. 3 shows a frequency-variation, temperature curve obtained for the same sample, which, by comparison with the curve of Fig. 1 shows the degree of aperiodicity obtained by the means described. Not only have the three discontinuities of the curve I disappeared, but the whole of the curve is raised and remains positive on its greater portion. This curve, shown in Fig. 3, il lustrates the effect of a thickness of @3 mm. of stopper placed between the jar acting as a support and the disc of piezoelectric quartz. In many cases where an approximation of this kind is suificient, one can rest content with resting the quartz plate on relatively soft metals such as lead or tin or a mixture of the two or the like which play the part of the viscous block mentioned in the above description.

The provision of these layers of soft metals may be effected either by sufiiciently thick tinning of the jar serving as resting place for the quartz plate or by any other suitable means depending on the desired method of support of the quartz. One arrangement is shown in Fig. 4 in which 1 represents the base support which comprises a threaded cylinder 2, and 3 the cover of suitable shape screwing in to an insulating ring 4 mounted on base I. This cover 3 tightens, by means of a spring with four double blades and a disc 6, the quartz plate 1 whose circumference is bevelled as indicated at 8. The lowest surface of plate 1 contacts with the upper plane surface of the threaded cylinder 2 and the bevelled flange 8 with a correspondingly bevelled edge of a threaded ring 9. The ring is screwed onto the cylinder 2 and can thus be approximately adjusted. The bevelled flange of the ring 9 is covered in accordance with one of the features of the invention with a thickness of lead or tin with which the bevelled edge of the quartz plate 6 contacts and which takes the place of viscous block B of Fig. 2 to attenuate to a sufficient extent the harmful compressional vibration.

Figs. 5 and 6 show a piezoelectric resonator comprising a quartz support employing features of the invention. In this resonator, la represents a cylindrical glass sheath closed at its two ends by the two metal lids 2a and 3a.. A brass guide member 4a of trough shaped in cross-section has a flat surface 5a near its middle. The guide lu. is fastened to insulating blocks 6a and la pressed on the ends of the glass tube by lids 2a and 3a with the interposition of tightening washers 8a. and 9a. The guide member 4a, is fastened to these blocks by two rivets Ill and H. The purpose of lid 3a is to hold a tightening screw l2 which through the agency of a cylinder l3 firmly holds together block Ia and a supporting plate 14. Atmospheric moisture is kept out of the tube by means of washer provided between the lid 3a and the insulating block 7a.

The supporting plate M consists of a plane plate adjustable by a suitable folded portion 2| and having at its end a supporting point l6. This point l6, as more clearly shown in Fig. 6, passes between two leaf springs l"! soldered at one end to the plate l4 and carrying at their free ends short contact points l8. These contact points l8 engage the metallized surfaces of the quartz plate 20. Another pivot point like I6 is carried by the guide member 4a. To guide 4a are soldered two leaf springs like I! provided with contact points like IS.

The plate of piezoelectric quartz 2!] is engaged at its middle point by the two opposite pivots constituting a well defined elastic support corresponding to B, S and P of Fig. 2 and 5, 8, 9 of Fig. 4.

If the quartz plate is so long that the middle support is insufficient to hold it in equilibrium during transport, tam-pings 23 of frayed natural sill; or other substances may be provided inside the tube at its ends.

By means of the supporting points l6 and the contact points l8 the damping of the crystal may be controlled in a predetermined manner. If minimum damping is desired then the contact points 58 are placed on the neutral axis of vibration of the crystal, which, in the case of a crystal vibrating longitudinally is inclined at an angle of 90 to the largest dimension of the crystal.

Fig. I shows another embodiment of a piezoelectric resonator. In this resonator, lb represents a glass sheath and 2b and 3b represent the metal lids separated from the ends of the sheath lb by insulating washers 4b and 5b provided with suitable openings to permit the passage of the connecting posts 8b and 6'. lb is an adjusting screw which also passes through a larger opening of the lid 31). The insulating washers 4b and 51) press elastic washers 8b against the edges of glass tube lb to make the apparatus moisture-proof. The terminals 6b and 6' serve also to fix guide member 9b in position along the side of the sheath lb. The bent up ends llJb of the member 9b are pressed by the terminals lib between the insulating washers 4b and 5b and insulating blocks lib and l2b. The lower terminals Eb are threaded and an assembly member |3b is held in the insulating block llb into which the terminals screw. A pin Mb projecting from lid 2b facilitates the setting in place of the latter.

At its middle point the guide member 9b carries a pivot point l5 engaging the quartz plate I922. The quartz plate passes between two flexible leaf springs lfib each provided at its end with a contact point l'ib and connected to the terminals 6b by means of rigid rods IBb, only one of which is shown. In the same way on the other side of the quartz plate l9b, two flexible blades 20?) are provided with points 2lb at their ends and connected to the terminal screws 6b by means of rods 22b. A single pivot point 23b carried by a leaf spring 24 passes between the springs 20b. The spring 24 is bent and fixed to the insulating block l2b by a rivet 25 and is provided with an opening 26 through which passes the end of the adjusting screw lb, a shoulder of which engages the edge of the opening.

The adjusting device of the resonator is more clearly shown in Fig. 9, in which the references correspond to those of Fig. 7. If the quartz plate, when first set in position, occupies the position l9 shown in dotted lines, which is inclined to the axis of the resonator, and if the pivot point carried by the leaf spring 24 is at 23' shown in dotted lines, then the angular deflection of the plate l9b may be compensated by adjusting the screw lb. The rear end of spring 24 is bent back to form with the free end an angle [3 which is determined by an initial adjustment to insure the pressing of the quartz plate l9b against the points l5b and 23b. The angle a between the rear end of spring 24 and the insulating block l2b to which it is fixed may be varied by means of the adjusting screw lb. By shifting point 23 with respect to the fixed point I529 the plate l9b will be rotated at the desired angle until it is parallel to axis of the system. In the case illustrated in the drawings, the adjusting screw lb must be screwed in to move the point 23?] from its position 23' to the right.

As in the piezoelectric device shown in Figs. and 6, the ends of the piezoelectric plate 59 may be embedded in frayed natural silk or any other suitable substance to permit transportation of the resonators without disturbing the equilibrium of the quartz plate. In certain cases this does not cause harmful damping and may be permanently retained in. the device.

The invention is not restricted to the examples specifically described and is capable of other applications which will appear to those skilled in the art.

What is claimed is:

1. In combination a piezoelectric crystal element an edge support for the crystal element and a layer of lead, tin or other soft metal on said edge support and forming a bearing for said crystal element.

2. In combination a circular plate of piezoelectric material a bevelled peripheral edge thereon and a soft metal seating for said bevelled edge.

3. In combination a disc of piezoelectric crystal, electrically conducting supports engaging the faces of said disc, means for resiliently urging the supports together and means attached to one of said supports for damping lateral movement at the periphery of the disc.

4. In combination a circular plate of piezoelectric material, a bevelled edge thereon, electrodes engaging the faces of said plate, means for resiliently urging said electrodes together, a bevelled ring upon one of said electrodes surrounding said plate and a layer of soft metal between and in contact with said bevelled edge and said bevelled ring.

5. In the arrangement according to claim 4 means for axially adjusting said bevelled ring.

MARC ERNEST ALBERT BRUZAU. STANISLAS VAN MIERLO. PAUL LUCIEN BOUR. 

